You're in canada so our placement on google.ca may well be different than google.com in US. There are some day to day fluctuations in position as google is served from many different servers and it takes a while for them to synchronize which is why some people are seeing #1, #3, and #4 ranking. Seems like the #1 was a fluke or a temporary thing with #3 being the average rank I and others have seen lately. This is fantastic considering this consists of over 3 million search results. The most important thing is being in the top half of the screen in search results so users can click at first glance rather than having to scroll down.
That being said, the two things you can do to help the forum rank better on google:
A) Participate. Believe it or not, the more you write, the more topics you start, the more questions you answer, the more content we have and google gives more priority to such sites and we can appear in specific search queries such as "how to teach my parrot to step up?"
B) Link to http://theparrotforum.com from wherever you can online. If you have a personal site, blog, youtube channel, etc. The more websites that link to theparrotforum, the higher the google page rank and the higher it gets placed in search results.
Basically the more active the forum and the more people that like the forum, the better it ranks in search results, the more people that find it, etc. The hard part is to get it rolling. Once it does, there's no stopping it.